Deriving Relations Between Physical Quantities

Deriving Relations Between Physical Quantities

If a physical quantity depends on other quantities, dimensional analysis can be used to find the possible relation.

### General Formula

If: $$Q\propto a^xb^yc^z$$

then:

$$[Q]=[a]^x[b]^y[c]^z$$

### Terminologies

- Q → Dependent physical quantity.

- a, b, c → Independent physical quantities.

- x, y, z → Unknown powers.

### Conditions / Special Cases

- Numerical constants cannot be determined using dimensional analysis.

- Trigonometric, exponential, and logarithmic functions cannot be handled using dimensional analysis.

### Usage

- Used for deriving formulas involving powers of physical quantities.